Estimating the effective reproduction number of COVID-19 from population-wide wastewater data: An application in Kagawa, Japan.

Although epidemiological surveillance of COVID-19 has been gradually downgraded globally, the transmission of COVID-19 continues. It is critical to quantify the transmission dynamics of COVID-19 using multiple datasets including wastewater virus concentration data. Herein, we propose a comprehensive method for estimating the effective reproduction number using wastewater data. The wastewater virus concentration data, which were collected twice a week, were analyzed using daily COVID-19 incidence data obtained from Takamatsu, Japan between January 2022 and September 2022. We estimated the shedding load distribution (SLD) as a function of time since the date of infection, using a model employing the delay distribution, which is assumed to follow a gamma distribution, multiplied by a scaling factor. We also examined models that accounted for the temporal smoothness of viral load measurement data. The model that smoothed temporal patterns of viral load was the best fit model (WAIC = 2795.8), which yielded a mean estimated distribution of SLD of 3.46 days (95% CrI: 3.01-3.95 days). Using this SLD, we reconstructed the daily incidence, which enabled computation of the effective reproduction number. Using the best fit posterior draws of parameters directly, or as a prior distribution for subsequent analyses, we first used a model that assumed temporal smoothness of viral load concentrations in wastewater, as well as infection counts by date of infection. In the subsequent approach, we examined models that also incorporated weekly reported case counts as a proxy for weekly incidence reporting. Both approaches enabled estimations of the epidemic curve as well as the effective reproduction number from twice-weekly wastewater viral load data. Adding weekly case count data reduced the uncertainty of the effective reproduction number. We conclude that wastewater data are still a valuable source of information for inferring the transmission dynamics of COVID-19, and that inferential performance is enhanced when those data are combined with weekly incidence data.